You'll be able to make all new elections, if you choose CSRS Offset coverage. If you decide to waive your military retired pay, you will be able to waive it back to your retirement date. Also, you'll have an opportunity to pay the military deposit. Since you owed a FERS military deposit when you were in FERS and would owe a larger CSRS deposit if you choose CSRS Offset coverage, you can take an actuarial reduction in your annuity instead of paying the CSRS military deposit. The actuarial reduction is based on the amount of military deposit you owe and your age at retirement.
Before you're asked to choose retirement plans, OPM will give you information about your benefits under both CSRS Offset and FERS. They will tell you how much your military deposit is under both. They will also explain how payment of a military deposit and the actuarial reduction will affect your benefit.

No, you do not have to pay it back.
The lump sum benefit you received is known as the Basic Employee Death Benefit. It is equal to half of your spouse's final salary plus an additional amount. Surviving spouses choose whether they want to receive this benefit in a single payment or in equal installments over 36 months. This benefit is only available under FERS.
FERCCA has special rules for surviving spouses who choose CSRS Offset rather than FERS and were paid a Basic Employee Death Benefit. Instead of you paying it back, OPM will apply an actuarial reduction when it calculates your CSRS Offset survivor benefit.

Your make-up contributions will be invested based on your most recent contribution allocation. For example, if you currently allocated 75% of the TSP contributions withheld from your pay to go to the C Fund and 25% to go to the G Fund, your make-up contributions will be allocated in the same manner. If you don't have a contribution allocation on file with the Federal Retirement Thrift Investment Board, the make-up contributions will be invested in the G Fund.
You may also get lost earnings on your make-up contributions. The amount of the lost earnings you receive are based on the contribution allocation in effect at the time the make-up contributions would have been made had you been correctly covered by FERS. For example, suppose you are going to make-up contributions for the period January 11, 1995 to July 6, 1995. During that period you may had allocated 45% of the contributions withheld from your pay to go to the G Fund and 55% to go to the C Fund. The lost earnings on your make-up would be computed as though 45% of your make-up went to the G Fund in 1995 and 55% had gone to the C Fund.
If you didn't have a contribution allocation, the lost earnings will be based on the return of the G Fund.

Yes. If an employee dies before making an election of retirement coverage under FERCCA, all eligible potential survivors, that is both the current and any former spouses, must consent to an election of FERS coverage. If they do not all consent, the election cannot be made.

No. The Social Security Law also includes a provision -- the Windfall Elimination Provision (WEP) -- that reduces Social Security benefits for individuals who have less than 30 years of "substantial earnings" under Social Security and who have earned a retirement benefit from employment not covered by Social Security; for example, CSRS service. The WEP was designed to eliminate the "windfall" that could result if you were to receive a CSRS annuity based on many years of employment not covered by Social Security and also receive a full Social Security benefit because you had a few years of employment covered under Social Security. The WEP, however, never totally eliminates the Social Security benefit you have earned. For example, in 2001, the maximum amount the WEP can decrease a Social Security benefit is $280.50 per month. For more information, see SSA's The Windfall Elimination Provision at http://www.ssa.gov/pubs/10045.html.

If you are erroneously covered by FERS and you choose to move out of FERS, FERCCA allows you to keep the employee contributions you made in your TSP account (plus the earnings attributable to your contributions) even if the contributions exceed 5 percent of the basic pay you earned for the pay period that contributions had been made. However, all Government contributions that were made to your account and the attributable earnings must be removed from your account if you do not choose FERS.
If you choose FERS coverage under FERCCA, you may make up those employee contributions that you could have made had you been correctly covered by FERS, as provided by the current TSP error correction legislation. In addition, you will receive the agency automatic (1%) contributions and agency matching contributions that you should have received had you been correctly covered by FERS. Finally, you will receive lost earnings on both your employee and agency make-up contributions. (Prior to FERCCA, lost earnings were payable only on agency make-up contributions.) The lost earnings on both employee and agency contributions will be determined the same way lost earnings are now determined on agency make-up contributions (that is, as provided by the current TSP regulations).

Except for the last 3 years, the money you erroneously paid into Social Security will remain to your credit in the Social Security fund. The Social Security Administration will include all but those last 3 years in determining your eligibility for, and the amount of, future benefits.
The amount you paid into Social Security for the last 3 years will be transferred to your account in the Civil Service Retirement fund. Your employing agency will pay all additional retirement contributions owed for your CSRS time. It may not go back and bill you for additional retirement deductions when it corrects the error.

Actually, you're probably better off in CSRS Offset because you're earning benefits under both Social Security and CSRS.
Your combined benefits under Social Security and CSRS Offset will be at least the same as, if not more than, what you would have received under Social Security and CSRS if your record had not been corrected.
While working, you are earning retirement credits under the relatively generous CSRS formula. You also are adding to any Social Security benefits you have already earned, increasing your career earnings under Social Security and, as a result, your Social Security benefit.
When you retire, OPM will compute your CSRS Offset benefit under the same rules that apply to other CSRS retirees. When you become eligible for Social Security benefits, OPM will reduce your benefit. This reduction is based on the value of the Social Security benefit you earned during your CSRS Offset service. In other words, instead of getting one check from OPM for all of your Federal service, some of the payment will come from the Social Security Administration.
In addition, with more of your retirement income paid from Social Security, you have an increased tax advantage because part, or all, of your Social Security benefit will be exempt from Federal income tax. Only a small portion of a CSRS, or CSRS Offset, benefit is exempt from Federal income tax.

It depends on when you withdrew your TSP contributions and the kind of withdrawal you made.
You can make an election under FERCCA if you:

Separated from Government service after your agency corrected your records—but you did not retire—and the TSP automatically paid your account balance to you because it was $3,500 or less;

Retired and withdrew your TSP contributions; or

Received a financial hardship in-service withdrawal, or a TSP loan.

You cannot make an election under FERCCA if you:

Separated from Government service after your agency corrected your records—but you did not retire—and you withdrew your TSP contributions. This does not include the TSP automatic payment described above; or

Received an age-based in-service withdrawal from your TSP account while employed.

You will get Social Security credit for all that work, and it won't cost you anything. Your agency will send the Social Security Administration a record of your earnings during all the years you should have had Social Security coverage. All of the CSRS contributions you made during those years that are not needed to cover your retirement costs will be transferred to Social Security. This transfer will pay all the Social Security taxes you owe.

Under OPM regulations your agency makes retirement coverage decisions. OPM sends the letter to your agency so that your agency can review the information. Once your agency reviews the letter and confirms our findings, they send a final decision letter to you. The decision from your agency that your retirement coverage is correct, in other words that you are ineligible for relief under FERCCA, may be appealed to the Merit Systems Protection Board (MSPB), if you choose to do so.